A Hybrid System Based on Dynamic Selection for Time Series Forecasting

MR-Transformer: Multiresolution Transformer for Multivariate Time Series Prediction

Multivariate time series (MTS) prediction has been studied broadly, which is widely applied in real-world applications. Recently, transformer-based methods have shown the potential in this task for their strong sequence modeling ability. Despite progress, these methods pay little attention to extracting short-term information in the context, while short-term patterns play an essential role in reflecting local temporal dynamics. Moreover, we argue that there are both consistent and specific characteristics among multiple variables, which should be fully considered for MTS modeling. To this end, we propose a multiresolution transformer (MR-Transformer) for MTS prediction, modeling MTS from both the temporal and the variable resolution. Specifically, for the temporal resolution, we design a long short-term transformer. We first split the sequence into nonoverlapping segments in an adaptive way and then extract short-term patterns within segments, while long-term patterns are captured by the inherent attention mechanism. Both of them are aggregated together to capture the temporal dependencies. For the variable resolution, besides the variable-consistent features learned by long short-term transformer, we also design a temporal convolution module to capture the specific features of each variable individually. MR-Transformer enhances the MTS modeling ability by combining multiresolution features between both time steps and variables. Extensive experiments conducted on real-world time series datasets show that MR-Transformer significantly outperforms the state-of-the-art MTS prediction models. The visualization analysis also demonstrates the effectiveness of the proposed model.

Modeling and forecasting carbon dioxide emission in Pakistan using a hybrid combination of regression and time series models

Carbon dioxide (CO2) emissions continue to rise globally despite efforts to combat climate change. Energy industry emissions are a pressing global issue, causing devastating impacts. Hence, it is vital to accurately and efficiently forecast CO2 emissions. Thus, this study comprehensively analyzes forecasting CO2 emissions by comparing various hybrid combinations of regression and time series methods to explore the CO2 emissions in Pakistan. First, divide the yearly time series of CO2 emissions into the long-run curve trend series and the residual subseries. The long-run curve trend subseries is modeled using parametric and nonparametric regression methods, while various standard time series models are used to forecast the residual subseries. However, the forecasts of each subseries will be combined to obtain the final forecast of CO2 emissions. This work used four different accuracy mean errors, a statistical test, and a graphical analysis as performance measures to evaluate the proposed hybrid forecasting technique. The findings confirmed that the proposed hybrid combination forecasting technique is highly accurate and efficient in forecasting CO2 emissions. Likewise, according to the proposed final optimal hybrid combination forecasting model, Pakistan's per capita CO2 emissions will be 1.130215 metric tons in 2030. Pakistan's escalating emission trend signals that creative solutions must be implemented to curb it. Thus, the government must price carbon footprints, regulate electricity from zero-carbon sources, reduce population, encourage afforestation in densely populated areas, adopt clean technology, and fund research.

Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ0-Norm Minimization

Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and their investment percentages based on the sliding window approach. However, many existing algorithms for sparse index tracking cannot explicitly and directly control the number of assets or the tracking error. This article formulates sparse index tracking as two constrained optimization problems and then proposes two algorithms, namely, nonnegative orthogonal matching pursuit with projected gradient descent (NNOMP-PGD) and alternating direction method of multipliers for l0 -norm (ADMM- l0 ). The NNOMP-PGD aims at minimizing the tracking error subject to the number of selected assets less than or equal to a predefined number. With the NNOMP-PGD, investors can directly and explicitly control the number of selected assets. The ADMM- l0 aims at minimizing the number of selected assets subject to the tracking error that is upper bounded by a preset threshold. It can directly and explicitly control the tracking error. The convergence of the two proposed algorithms is also presented. With our algorithms, investors can explicitly and directly control the number of selected assets or the tracking error of the resultant portfolio. In addition, numerical experiments demonstrate that the proposed algorithms outperform the existing approaches.

Blood Glucose Level Time Series Forecasting: Nested Deep Ensemble Learning Lag Fusion

Blood glucose level prediction is a critical aspect of diabetes management. It enables individuals to make informed decisions about their insulin dosing, diet, and physical activity. This, in turn, improves their quality of life and reduces the risk of chronic and acute complications. One conundrum in developing time-series forecasting models for blood glucose level prediction is to determine an appropriate length for look-back windows. On the one hand, studying short histories foists the risk of information incompletion. On the other hand, analysing long histories might induce information redundancy due to the data shift phenomenon. Additionally, optimal lag lengths are inconsistent across individuals because of the domain shift occurrence. Therefore, in bespoke analysis, either optimal lag values should be found for each individual separately or a globally suboptimal lag value should be used for all. The former approach degenerates the analysis's congruency and imposes extra perplexity. With the latter, the fine-tunned lag is not necessarily the optimum option for all individuals. To cope with this challenge, this work suggests an interconnected lag fusion framework based on nested meta-learning analysis that improves the accuracy and precision of predictions for personalised blood glucose level forecasting. The proposed framework is leveraged to generate blood glucose prediction models for patients with type 1 diabetes by scrutinising two well-established publicly available Ohio type 1 diabetes datasets. The models developed undergo vigorous evaluation and statistical analysis from mathematical and clinical perspectives. The results achieved underpin the efficacy of the proposed method in blood glucose level time-series prediction analysis.

Forecasting blood demand for different blood groups in Shiraz using auto regressive integrated moving average (ARIMA) and artificial neural network (ANN) and a hybrid approaches

Providing fresh blood to keep people in need of blood alive, has always been a main issues of health systems. Right policy-making in this area requires accurate forecasting of blood demand. The current study aimed at predicting demand for different blood groups in Shiraz using Auto Regressive Integrated Moving Average (ARIMA), Artificial Neural Network (ANN) and a hybrid approaches. In the current time series analysis, monthly data of the Shiraz hospitals and medical centers demand for 8 blood groups during 2012-2019 were gathered from Shiraz branch of Iranian Blood Transfusion Organization. ARIMA, ANN and a hybrid model of them was used for prediction. To validate and comprise ARIMA and ANN models, Mean Square Error (MSE) and Mean Absolute Error (MAE) criteria were used. Finally, ARIMA, ANN and hybrid model estimates were compared to actual data for the last 12 months. R3.6.3 were used for statistical analysis. Based on the MSE and MAE of models, ARIMA had the best prediction for demand of all blood groups except O+ and O-. Moreover, for most blood groups, ARIMA had closer prediction to actual data. The demand for four blood groups (mostly negative groups) was increasing and the demand for other four blood groups (mostly positive ones) was decreasing. All three approaches including ARIMA, ANN and the hybrid of them predicted an almost downward trend for the total blood demand. Differences in the performance of various models could be due to the reasons such as different forecast horizons, daily/month/annual data, different sample sizes, types of demand variables and the transformation applied on them, and finally different blood demand behaviors in communities. Advances in surgical techniques, fetal screening, reduction of accidents leading to heavy bleeding, and the modified pattern of blood request for surgeries appeared to have been effective in reducing the demand trend in the current study. However, a longer time period would certainly provide more accurate estimates.

Solar Irradiance Forecasting Using Dynamic Ensemble Selection

Solar irradiance forecasting has been an essential topic in renewable energy generation. Forecasting is an important task because it can improve the planning and operation of photovoltaic systems, resulting in economic advantages. Traditionally, single models are employed in this task. However, issues regarding the selection of an inappropriate model, misspecification, or the presence of random fluctuations in the solar irradiance series can result in this approach underperforming. This paper proposes a heterogeneous ensemble dynamic selection model, named HetDS, to forecast solar irradiance. For each unseen test pattern, HetDS chooses the most suitable forecasting model based on a pool of seven well-known literature methods: ARIMA, support vector regression (SVR), multilayer perceptron neural network (MLP), extreme learning machine (ELM), deep belief network (DBN), random forest (RF), and gradient boosting (GB). The experimental evaluation was performed with four data sets of hourly solar irradiance measurements in Brazil. The proposed model attained an overall accuracy that is superior to the single models in terms of five well-known error metrics.

Ensemble streamflow forecasting based on variational mode decomposition and long short term memory

Reliable and accurate streamflow forecasting plays a vital role in the optimal management of water resources. To improve the stability and accuracy of streamflow forecasting, a hybrid decomposition-ensemble model named VMD-LSTM-GBRT, which is sensitive to sampling, noise and long historical changes of streamflow, was established. The variational mode decomposition (VMD) algorithm was first applied to extract features, which were then learned by several long short-term memory (LSTM) networks. Simultaneously, an ensemble tree, a gradient boosting tree for regression (GBRT), was trained to model the relationships between the extracted features and the original streamflow. The outputs of these LSTMs were finally reconstructed by the GBRT model to obtain the forecasting streamflow results. A historical daily streamflow series (from 1/1/1997 to 31/12/2014) for Yangxian station, Han River, China, was investigated by the proposed model. VMD-LSTM-GBRT was compared with respect to three aspects: (1) feature extraction algorithm; ensemble empirical mode decomposition (EEMD) was used. (2) Feature learning techniques; deep neural networks (DNNs) and support vector machines for regression (SVRs) were exploited. (3) Ensemble strategy; the summation strategy was used. The results indicate that the VMD-LSTM-GBRT model overwhelms all other peer models in terms of the root mean square error (RMSE = 36.3692), determination coefficient (R2 = 0.9890), mean absolute error (MAE = 9.5246) and peak percentage threshold statistics (PPTS(5) = 0.0391%). The addressed approach based on the memory of long historical changes with deep feature representations had good stability and high prediction precision.

Hybrid systems using residual modeling for sea surface temperature forecasting

The sea surface temperature (SST) is an environmental indicator closely related to climate, weather, and atmospheric events worldwide. Its forecasting is essential for supporting the decision of governments and environmental organizations. Literature has shown that single machine learning (ML) models are generally more accurate than traditional statistical models for SST time series modeling. However, the parameters tuning of these ML models is a challenging task, mainly when complex phenomena, such as SST forecasting, are addressed. Issues related to misspecification, overfitting, or underfitting of the ML models can lead to underperforming forecasts. This work proposes using hybrid systems (HS) that combine (ML) models using residual forecasting as an alternative to enhance the performance of SST forecasting. In this context, two types of combinations are evaluated using two ML models: support vector regression (SVR) and long short-term memory (LSTM). The experimental evaluation was performed on three datasets from different regions of the Atlantic Ocean using three well-known measures: mean square error (MSE), mean absolute percentage error (MAPE), and mean absolute error (MAE). The best HS based on SVR improved the MSE value for each analyzed series by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$82.26\%$$\end{document}82.26%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$98.93\%$$\end{document}98.93%, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$65.03\%$$\end{document}65.03% compared to its respective single model. The HS employing the LSTM improved \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$92.15\%$$\end{document}92.15%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$98.69\%$$\end{document}98.69%, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$32.41\%$$\end{document}32.41% concerning the single LSTM model. Compared to literature approaches, at least one version of HS attained higher accuracy than statistical and ML models in all study cases. In particular, the nonlinear combination of the ML models obtained the best performance among the proposed HS versions.

Forecasting COVID-19 recovered cases with Artificial Neural Networks to enable designing an effective blood supply chain

This study introduces a forecasting model to help design an effective blood supply chain mechanism for tackling the COVID-19 pandemic. In doing so, first, the number of people recovered from COVID-19 is forecasted using the Artificial Neural Networks (ANNs) to determine potential donors for convalescent (immune) plasma (CIP) treatment of COVID-19. This is performed explicitly to show the applicability of ANNs in forecasting the daily number of patients recovered from COVID-19. Second, the ANNs-based approach is further applied to the data from Italy to confirm its robustness in other geographical contexts. Finally, to evaluate its forecasting accuracy, the proposed Multi-Layer Perceptron (MLP) approach is compared with other traditional models, including Autoregressive Integrated Moving Average (ARIMA), Long Short-term Memory (LSTM), and Nonlinear Autoregressive Network with Exogenous Inputs (NARX). Compared to the ARIMA, LSTM, and NARX, the MLP-based model is found to perform better in forecasting the number of people recovered from COVID-19. Overall, the findings suggest that the proposed model is robust and can be widely applied in other parts of the world in forecasting the patients recovered from COVID-19.